Flywheel Inertia Calculator & Simulator

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🚀 Flywheel Inertia Calculator & Simulator

FLYWHEEL ENERGY

Flywheel Energy Storage and Pulsation Damping Simulator
DYNAMICS MODEL ACTIVE

Physical Design Parameters

(1.0 ~ 500.0 kg)
kg
(0.10 ~ 2.00 m)
m
(0.00 ~ 1.80 m)
m
(100 ~ 5000 RPM)
RPM
(10 ~ 5000 J)
J

Equipment Inertia Presets

Real-time Rotational Pulsation & Acceleration/Deceleration Chart

Pulsation Control Status: Normal Smooth Operation
Moment of Inertia (I) 20.80 kg·m²
Rotational Speed Variation (Min ~ Max) 1180 ~ 1220 RPM
Real-time Coefficient of Speed Fluctuation (Cf) 0.034
Stored Average Kinetic Energy (Ek)
164.2 kJ
Rotational Speed Ripple: 3.4% (Cf = 0.034)
Moment of Inertia (I) 20.80 kg·m²
Max / Min Operating Speed 1220 / 1180 RPM
System Suitability Evaluation Suitable (Highly Stable)

Flywheel Dynamics Formulas

I = 0.5 × M × (Ro^2 + Ri^2)
Cf = ΔE / (I × ω^2)
Disclaimer: The calculation results of this simulator are provided for educational and reference purposes only. For actual product design or manufacturing, please verify with the latest engineering codes and official standard design criteria. The integrity of the calculated values is not guaranteed, and the developer and this blog assume no liability for any direct or indirect damages arising from their use.
💡 💡 Quick User Guide
  1. Flywheel Geometry Design: Adjust the outer radius (Ro), inner radius (Ri), and mass (M) sliders to match your component geometry. (The moment of inertia is automatically calculated.)
  2. Set Average Operating RPM: Enter the average operating speed (N) of the system.
  3. Input Fluctuating Energy Load: Specify the fluctuation in rotational energy (dE) that occurs during one crankshaft cycle. (Typically, this is larger for single-cylinder engines.)
  4. Check Real-Time Rotational Pulsation & Damping: Watch the flywheel rotate in the 2D simulator. If the inertia is small or the fluctuating energy is large, you can visually observe the pulsation phenomenon (Cf visualization), where the rotational speed fluctuates and undergoes severe acceleration and deceleration.
  5. Analyze Speed Fluctuation Graph: Compare and observe the damping of the flywheel speed’s pulsation waveform in real-time to determine if sufficient inertia has been secured to remain within the target coefficient of speed fluctuation.
📚 Detailed Mechanical Engineering Guide & Flywheel Design Standards ▼

1. Physical Role of the Flywheel in Internal Combustion Engines and Reciprocating Compressors

In reciprocating engines or single-cylinder crank presses, the torque generated varies significantly depending on the crank angle during the process of converting the linear motion of the piston into the rotational motion of the crankshaft. In a 4-stroke single-cylinder engine, massive torque is generated during the power stroke, but power is consumed during the remaining intake, compression, and exhaust strokes, causing the shaft rotational speed to fluctuate wildly.

A flywheel is a heavy rotating disc mounted on such rotational systems. Its role is to absorb and store surplus energy from the power stroke as rotational kinetic energy, and release this energy during the non-powered strokes to smooth out (dampen) the shaft’s rotational speed. In other words, it acts as a mechanical battery that temporarily stores rotational energy.

2. Formulas for Mass Moment of Inertia and Rotational Kinetic Energy

Generally, the moment of inertia (I) of a hollow cylindrical (rim-type) flywheel with a certain thickness is determined by its mass M, outer radius Ro, and inner radius Ri:

I = 1/2 · M · (Ro2 + Ri2)  [kg·m2]

The total rotational kinetic energy (Ek) stored at an average angular velocity ω = (2π · N) / 60 is as follows:

Ek = 1/2 · I · ω2  [Joule]

When a fluctuating energy load ΔE (the difference between energy supplied and consumed per crank cycle) is applied, the system’s coefficient of speed fluctuation (Cf) is derived as follows:

Cf = (Nmax – Nmin) / N  =  ΔE / (I · ω2)

3. Recommended Coefficient of Speed Fluctuation (Cf) Standards by Industrial Machinery

A lighter flywheel allows faster rotational acceleration but causes greater speed fluctuations. Conversely, an excessively heavy flywheel increases shaft bearing loads and material costs. Therefore, optimization based on application is essential:

  • AC Synchronous Generators for Power Gen. (Precise frequency control required): Cf ≤ 0.003 ~ 0.005 (0.3% ~ 0.5% fluctuation)
  • Precision Looms and Machine Tools: Cf ≤ 0.01 ~ 0.02 (1% ~ 2% fluctuation)
  • General Industrial Multi-cylinder Diesel Engines: Cf ≤ 0.03 ~ 0.05
  • Crushers and Air Compressors: Cf ≤ 0.05 ~ 0.10 (5% ~ 10% fluctuation allowed)

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